Problem: Igbo uploaded a funny video of his cat onto a website. The relationship between the elapsed time, $d$, in days, since the video was first uploaded, and the total number of views, $V(d)$, that the video received is modeled by the following function. $V(d)=10^{{1.5d}}$ How many days will it take for the video to receive $1{,}000{,}000$ views? Round your answer, if necessary, to the nearest hundredth.
Thinking about the problem We want to know how many days, $d$, it will take for the number of video views, $V(d)$, to reach $1{,}000{,}000$. So we need to find the value of $d$ for which $V(d)=1{,}000{,}000$. Substituting $1{,}000{,}000$ in for $V(d)$ in the function gives us the following equation. $1{,}000{,}000=10^{{1.5d}}$ Solving the equation We can solve the equation as shown below. $\begin{aligned}10^{1.5d}&=1{,}000{,}000\\\\ 1.5d&=\log(1{,}000{,}000)\\\\ d&=\dfrac{\log(1{,}000{,}000)}{1.5}\\\\ d&=4\end{aligned}$ It will take $4$ days for the video to receive $1{,}000{,}000$ views.